# Thread: Differentiating with respect to x^2 and 1/(1-x)... AP review problem

1. ## Differentiating with respect to x^2 and 1/(1-x)... AP review problem

I'm reviewing my first semester of AP Calculus. While doing some review questions, I came across these two problems.

1. If , find the derivative of with respect to .
2. If , find the derivative of with respect to .

I started manipulating the derivative notation in order to get the solution, but how do I continue this problem?

2. ## Re: Differentiating with respect to x^2 and 1/(1-x)... AP review problem

(1) $y = \sqrt{x^2+1}$

$y^2 = x^2 + 1$

$\frac{d}{dx^2}(y^2 = x^2 + 1)$

$\frac{dy^2}{dx^2}= 1$

(2) let $u = \frac{1}{1-x}$

$\frac{du}{dx} = \frac{1}{(1-x)^2}$

$y = x^2+x$

$\frac{dy}{dx} = 2x+1$

$\frac{dy}{du} = \frac{\frac{dy}{dx}}{\frac{du}{dx}} = (2x+1) \cdot (1-x)^2$